Word for terror at the idea of being infinitely born again into different bodies

I'm looking for a word that describes terror at the idea of being infinitely born back into the world, trapped in a cycle that never ends and is inescapable.

Possibly a word that relates to religion or philosophy.

There's no single word as far as I know. You might call it metaphysical dread/horror/panic to emphasize that the dread/horror/panic is rooted in a metaphysical possibility.

Nietzsche called the burden of experiencing your own life infinitely many times the greatest weight:

The greatest weight—What, if some day or night a demon were to steal after you into your loneliest loneliness and say to you: "This life as you now live it and have lived it, you will have to live once more and innumerable times more; and there will be nothing new in it, but every pain and every joy and every thought and sigh and everything unutterably small or great in your life will have to return to you, all in the same succession and sequence - even this spider and this moonlight between the trees, and even this moment and I myself. The eternal hourglass of existence is turned upside down again and again, and you with it, speck of dust!" (here)

The reason I mention this is because perhaps some of the literature on Nietzsche will contain a term describing the potential horror one feels at the idea of cyclic rebirth or the similar idea of eternal return.

As I suggested in a now deleted comment, you could use the word Samsaraphobia.

Please note that this is not an established word, by any means. (The adjective Samsaraphobic has been used a little bit online, but it's definitely not in any dictionary.)

Samsara: (Dharmic religions) The endless series of births, deaths, and rebirths to which all beings are subject.

Phobia: A persistent, irrational fear of a specific object, activity, or situation that leads to a compelling desire to avoid it.

Please note that even this word might not fully satisfy your criteria in OP.

This is due to your criterion:

a cycle that never ends and is inescapable.

The word "Samsara" stems from the Sanskrit language and the religious texts of Dharmic religions. In those religions, Samsara is not at all seen as inescapable. On the contrary, the major teaching of those religions is that Samsara is in fact escapable. Not only that, doing so is in fact the ultimate goal of those religions. Hence, samsara can by no means be described as something inescapable.

However, phobia can mean an "irrational" fear. So that might make sense, then.